Dynamic approximation of spatio-temporal receptive fields in nonlinear neural field models
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Submission date: 19. May. 2001
published in: Neural computation, 14 (2002) 8, p. 1801-1825
DOI number (of the published article): 10.1162/089976602760128027
Keywords and phrases: cortex, tuning, spatio-temporal receptive fields, neural field equations, dynamics, nonlinear approximation, meanfield model, receptive field reconstruction
I present an approximation method that reduces the spatio-temporal behavior of localized activation peaks (also called "bumps") in nonlinear neural field equations to a set of coupled ordinary differential equations (ODEs) for only the amplitudes and tuning widths of these peaks. This enables a simplified analysis of steady state receptive fields (RFs) and their stability as well as of spatio-temporal point spread functions and related dynamic tuning properties. The lowest order approximation for the peak amplitudes alone turns out to be equivalent to meanfield equations for randomly coupled pools of graded response or Poissonian neurons (e.g., the Wilson-Cowan oscillator for two pools). Thus, much of the well studied meanfield behavior should carry over to localized solutions in neural fields. I further show how full spatio-temporal response functions can be reconstructed from such meanfield approximations. To this end the response profiles are written as superpositions of roughly Gaussian components in space which are temporally modulated by coefficients which again can be obtained from a low-dimensional ODE.
The method is applied to two standard neural field models: a one-layer model with difference-of-Gaussians connectivity kernel and a two-layer excitatory-inhibitory network. Both models reveal identical steady states and saddle-node instabilities to high firing rates. The two-field model can also loose stability through a Hopf-bifurcation that results in rhythmically modulated tuning with frequencies from 0 to perhaps 50Hz. The network behavior of the two-layer model is largely independent of the relative weights and widths of the mutual coupling kernels between the excitatory and inhibitory cells. Formulas for tuning properties, instabilities, and oscillation frequencies are given and exemplary spatio-temporal reponse functions reconstructed from meanfield solutions are compared with full network simulations.